The step size \(\delta \)  and kernel bandwidth \(h\)  was chosen via a manual process so that SVGD on the highest level numerically converged. The same \(\delta \)  and \(h\)  are used for SVGD and MLSVGD. Time measurements were performed on compute nodes with Intel Xeon CPU E5-2690 v2, restricted to 8 cores and 32GB memory, with a Matlab implementation. The MCMC reference is computed with the delayed-rejection adaptive Metropolis (DRAM) method [1]}, [2]} on the highest level \(L\)  of the respective problem. The covariance matrix of the Gaussian proposal is initialized to be diagonal with \(10^{-2}\)  on the diagonal. The burn-in time is 10,000 samples. Another 20,000 samples are generated and every other sample is then used to compute the MCMC reference mean \(\bar{{\theta }}\)  of the parameter. The error reported in Figure REF a and Figure REF c is \(\frac{1}{10}\sum _{i = 1}^{10} \Vert \bar{{\theta }} - {\theta }^{(i)}\Vert _2\) , where \({\theta }^{(i)}\)  is the mean of (ML)SVGD particles of the \(i\) -th replicate.
